In a large mixing bowl stir together 1 cup of the flour and the yeast. In a medium saucepan heat and stir the water, milk, shortening, sugar, and salt just until warm (120 degrees F to 130 degrees F) and shortening almost melts. Stir in the potato flakes. Let stand for 1 minute. Add milk mixture to dry mixture along with the egg. Beat with an electric mixer on low to medium speed for 30 seconds, scraping the sides of the bowl. Beat on high speed for 3 minutes. Using a wooden spoon, stir in as much of the remaining flour as you can.

Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape dough into a ball. Place dough in a lightly greased bowl, turning once to grease surface of the dough. Cover and let rise in a warm place until double in size (about 1-1/4 hours).

Punch dough down. Turn dough onto a lightly floured surface. Divide the dough in half. Cover and let rest for 10 minutes. Lightly grease two 8x8x2-inch or 9x9x2-inch baking pans.

On a lightly floured surface, roll each portion of dough to 1/2-inch thickness. Cut dough with a floured 2-1/2-inch round cutter. Place rolls in prepared baking pans. Cover and let rise in a warm place until nearly double in size (30 to 40 minutes).

Bake in a 375 degree F oven for 15 to 20 minutes or until golden. Immediately remove rolls from pans. Cool the rolls on wire racks. Makes 20 to 24 rolls.

Before letting the shaped roll dough rise, cover shaped rolls in pan with oiled waxed paper, then with plastic wrap, and refrigerate for 2 to 24 hours. Remove from refrigerator and let stand, covered, at room temperature for 20 minutes. Bake following directions above. Or, up to 2 weeks ahead, prepare and bake the rolls. Wrap in moisture-vapor proof wrap and freeze.